Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / Section B / B8 / b / Solution

Between launch and interception, $\Delta x=v{t}_{\mathrm{out}}$. The time-coordinate Lorentz transformation therefore givesThis is an elapsed coordinate time in B's inertial frame, not the travel time on A's clock. The latter would be $t_{\mathrm{out}}/{\gamma }_u=3a/(\sqrt{7}c)$.